The present invention relates generally to the field of photonic crystals and more particularly to two-dimensional photonic crystal apparatus.
Photonic crystals (PC) are periodic dielectric structures which can prohibit the propagation of light in certain frequency ranges. Photonic crystals have spatially periodic variations in refractive index and with a sufficiently high contrast in refractive index, photonic bandgaps can be opened in the structure""s optical spectrum. The xe2x80x9cphotonic bandgapxe2x80x9d is the frequency range within which propagation of light through the photonic crystal is prevented. A photonic crystal that has spatial periodicity in three dimensions can prevent light having a frequency within the crystal""s photonic bandgap from propogating in any direction. However, fabrication of such a structure is technically challenging. A more attractive alternative is to utilize photonic crystal slabs that are two-dimensionally periodic dielectric structures of finite height that have a band gap for propagation in the plane and use index-confinement in the third dimension. In addition to being easier to fabricate, two-dimensional photonic crystal slabs provide the advantage that they are compatible with the planar technologies of standard semiconductor processing.
An example of a two-dimensional photonic crystal structure periodic in two dimensions and homogeneous in the third may be fabricated from a bulk material having a periodic lattice of circular air filled columns extending through the bulk material in the height direction and periodic in the planar direction. The propagation of light in two-dimensional photonic crystals is determined by a number of parameters, including radius of the cylindrical columns, the lattice spacing, the symmetry of the lattice and the refractive indices of the bulk and column material.
Introducing defects in the periodic structure of a photonic crystal allows the existence of localized electromagnetic states that are trapped at the defect site and that have resonant frequencies within the bandgap of the surrounding photonic crystal material. By providing a line of such defects in the photonic crystal, a waveguiding structure is created that can be used in the control and guiding of light (see, for example, J. D. Joannopoulos, R. D. Meade, and J. N. Winn, xe2x80x9cPhotonic Crystalsxe2x80x9d, Princeton University Press, Princeton, N.J., 1995). Light of a given frequency that is prevented from propagating in the photonic crystal may propagate in the defect region.
A two-dimensional photonic crystal slab waveguide usually comprises a two-dimensional periodic lattice in the form of an array of dielectric rods or air holes incorporated in a slab body. High guiding efficiency can be achieved only in a narrow frequency region close to the upper or lower edge (for dielectric rods or air holes, respectively) of the waveguide band, where there are no leaky modes. Typically, high guiding efficiency is achieved only in a narrow frequency region that is only a few percent of the center frequency of the waveguide band and existing configurations suffer from low group velocities in the allowed waveguide band. Low group velocity increases the unwanted effects of disorder and absorption. (see S. G. Johnson, S. Fan, P. R. Villeneuve, L. Kolodziejski and J. D. Joannopoulos, Phys. Rev. B 60,5751, 1999 and S. G. Johnson, P. R. Villeneuve, S. Fan and J. D. Joannopoulos, Phys. Rev. B 62,8212,2000).
FIG. 1 shows an xy view of prior art two-dimensional photonic crystal slab apparatus 100. Photonic crystal slab 115 has circular holes 110 arranged to from a periodic triangular lattice with a lattice spacing equal to a. Circular holes 110 are filled with air. Region of defects 125 is created by replacing circular holes 110 of the lattice with larger circular holes 120 along a line in the x direction. Ridge waveguide 175 couples light into photonic crystal slab apparatus 100 that may have its edge at line Axe2x80x2, line Bxe2x80x2 or line Cxe2x80x2 in FIG. 1.
FIG. 2 shows the transmission coefficient for two-dimensional crystal slab apparatus 100 as a function of frequency expressed in fractions of c/axe2x80x94where cxe2x80x94is the speed of lightxe2x80x94and a is the lattice spacing. The radius for circular holes 120 is about 0.45 a and the radius for circular holes 110 is about 0.3 a. Curve 210 represents the unguided case which has low transmission in the bandgap and high transmission in the allow band. Curve 201 represents the case where ridge waveguide 175 is attached to photonic crystal slab 15 at the edge defined by line A in FIG. 1. Curve 202 represents the case where ridge waveguide 175 is connected to photonic crystal slab 115 at the edge defined by line B in FIG. 1. Curve 203 represents the case where ridge waveguide 175 is connected to photonic crystal slab 115 at the edge defined by line Cxe2x80x2 in FIG. 2. The transmission for curve 203 is a maximum for a frequency of about 0.253 c/a and the waveguide band is narrow. Increasing the radius of circular holes 120 to 0.5 a causes circular holes 120 to touch and start to overlap. This results in rapid deterioration of the transmission properties of two-dimensional crystal slab apparatus 100 as the light wave becomes less confined due to the decrease of the average dielectric constant of two-dimensional crystal slab 100.
In accordance with the invention, noncircular holes such as elliptical holes or rectangular holes are introduced as defects in the guiding direction of the photonic-crystal slab to create wide wave guiding bands covering more than 10% of the center frequency portion of the waveguide band. The elliptical or rectangular holes form a line of defects in the photonic crystal slab. Because low group velocities occur at the edges of the waveguide bands where the band becomes flat there is a wider range of frequencies with high group velocities available. Elliptical and rectangular holes provide significantly wider waveguide bandwidth and higher group velocity than circular holes. Over 10% of guiding bandwidth is achieved for a wide range of elliptical and rectangular shapes. The presence of a wider range of operating frequencies gives more forgiving fabrication tolerance for practical waveguide and allows more design flexibility when stub tuners, add-drop filters, bends and splitters are added. Higher group velocity will also lower the propagation loss of the waveguide.